Linear autonomy conditions for the basic Lie algebra of a system of linear differential equations (Q736030)

In this short note, the author announces new linear autonomy conditions for the generators of basic Lie algebras associated to first order systems of linear differential equations with complex coefficients (extending the known real case [\textit{V. L. Ovsyannikov}, Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 5, 559--561 (1993; Zbl 0828.35006)]). The criteria are expressed in terms of certain properties of the characteristic equations of the coefficient matrices, and lead to an algorithm consisting of two steps. No proofs of the three announced theorems are given.